The following Watson's \(_8\phi _7\)  transformation (cf.[1]})
\(& _{8}\phi _{7}\!\left[\begin{array}{cccccccc}a,& qa^{\frac{1}{2}},& -qa^{\frac{1}{2}}, & b, & c, & d, & e, & q^{-N} \\& a^{\frac{1}{2}}, & -a^{\frac{1}{2}}, & aq/b, & aq/c, & aq/d, & aq/e, & aq^{N+1}\end{array};q,\, \frac{a^2q^{N+2}}{bcde}\right] \\[5pt]&\quad =\frac{(aq, aq/de;q)_N}{(aq/d, aq/e;q)_N}\,{}_{4}\phi _{3}\!\left[\begin{array}{c}aq/bc,\ d,\ e,\ q^{-N} \\aq/b,\, aq/c,\, deq^{-N}/a\end{array};q,\, q\right]\) 
